HyperSolver: A Practical Unified Framework for Large-Scale Combinatorial Optimization
Bibliographic record
Abstract
We present HyperSolver, a unified hypergraph neural network framework for solving NP-hard combinatorial optimization problems using a single neural network architecture. Traditional approaches require different algorithms for each problem, while HyperSolver uses the same architecture across multiple minimization and maximization problems, including set cover, hitting set, subset sum, hypergraph max cut, and hypergraph multiway cut. We represent each problem instance as a hypergraph, where hyperedges can connect multiple nodes simultaneously to capture multi-element relationships directly. HyperSolver learns through unsupervised training using problem-specific loss functions without requiring pre-computed solutions or labeled training data. We evaluated HyperSolver on synthetic benchmark datasets with controlled structural parameters and compared its performance to commercial solvers, traditional heuristics, and existing hypergraph neural network methods. HyperSolver consistently computes high-quality solutions with significant speedups over exact methods, traditional heuristics, and competing neural approaches. The framework demonstrates effective knowledge transfer across problem types, where models trained on one problem accelerate training on different problems while maintaining solution quality. These results establish HyperSolver as a practical unified alternative to problem-specific solvers for large-scale combinatorial optimization.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".